Finite Group DatabasebetaFinite Group Databasebeta| order | 23200 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 71680 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C4 |
| abelian | C4×C8×C25×C29 |
| multiplicative | (ℤ/23533)ˣ, (ℤ/29005)ˣ, (ℤ/29125)ˣ, (ℤ/47066)ˣ, (ℤ/58010)ˣ, (ℤ/58250)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C4×C5 | C22×C5×C29 |
| socle, prime radical | C22×C5×C29 | C2×C4×C5 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
132 conjugacy classes of subgroups.
23200 conjugacy classes. The character table is too large to display.
| automorphism group of | C101×C233 |
| outer automorphism group of | C101×C233 |
Past the SmallGroups library coverage — no SmallGroups id.